We introduce a new model of traffic flow with phase transitions. The model is obtained by coupling together the classical Lighthill-Whitham-Richards (LWR) equation with the 2 × 2 system described in [A. Aw and M. Rascle, Resurrection of “second order” models of traffic flow, SIAM J. Appl. Math., 60 (2000), pp. 916–938]. We describe the solutions of the Riemann problem, and we compare the result...

The classical Lighthill-Whitham-Richards (LWR) kinematic traffic model is extended to a unidirectional road on which the maximum density a(x) represents road inhomogeneities, such as variable numbers of lanes, and is allowed to vary discontinuously. The car density φ = φ(x, t) is then determined by the following initial value problem for a scalar conservation law with a spatially discontinuous ...

Howickia Richards 1951 is redefined to include all wingless or strongly brachypterous Sphaeroceridae in New Zealand as well as two newly described fully winged species, H. oliveri and H. lepidostylus. Biroina Richards 1973 is newly treated as a junior subjective synonym of Howickia. The following new flightless species are described from New Zealand: H. bicolor, H. cordata, H. exasperata, H. ha...

First order traffic flow models have been studied for long time, since they represent the simplest way to begin with the understanding of such a complex system. To our knowledge the Lighthill-Whitham-Richards (LWR) model was the first model to describe unidirectional, one-dimensional traffic flow in a highway [1], [2]. This model considers the continuity equation for the density of vehicles (nu...

To address the subject of women and nutrition, it is necessary to work across disciplines. There is a long tradition of nutritionists and anthropologists working together in the United States, thanks to the pioneering work of Margaret Mead in this area. In Britain, the collaboration began even earlier with Audrey Richards (1932) in the 1930s. This collaboration continues today in the Economic a...

To address the subject of women and nutrition, it is necessary to work across disciplines. There is a long tradition of nutritionists and anthropologists working together in the United States, thanks to the pioneering work of Margaret Mead in this area. In Britain, the collaboration began even earlier with Audrey Richards (1932) in the 1930s. This collaboration continues today in the Economic a...

Mathematical results are presented that strongly constrain the prototypification of complex shape. Such shape requires local prototypification in two senses: (1) prototypification occurs in parallel at different parts of the figure, and (2) prototypification varies diferentially (smoothly) across an individual part. With respect to (l), we present a theorem that states that every Hoffman-Richar...

How to estimate queue length in real-time at signalized intersection is a long-standing problem. The problem gets even more difficult when signal links are congested. The traditional input–output approach for queue length estimation can only handle queues that are shorter than the distance between vehicle detector and intersection stop line, because cumulative vehicle count for arrival traffic ...

The traditional Richards' equation implies that the wetting front in unsaturated soil follows Boltzmann scaling, with travel distance growing as the square root of time. This study proposes a fractal Richards' equation (FRE), replacing the integer-order time derivative of water content by a fractal derivative, using a power law ruler in time. FRE solutions exhibit anomalous non-Boltzmann scalin...

This note is a sequel to the paper On rings on rings by Anatole Beck [ l ] . The problem we consider (originally proposed by Paul Rosenbloom) is that of characterizing the parameter p for the annulus Q = {1< | s| <p} in terms of the ring R of bounded analytic functions nn this annulus. Beck's solution involves properties of univalent functions, and although the subset of univalent functions in ...